Optimal Pruning Research Articles

DETERMINATION OF THE OPTIMAL SHOOT LENGTH AND PRUNING STRATEGIES IN 'BOURJASOTTE NOIRE' FIG

ISHS XXVIII International Horticultural Congress on Science and Horticulture for People (IHC2010): International Symposium on the Challenge for a Sustainable Production, Protection and Consumption of Mediterranean Fruits and Nuts DETERMINATION OF THE OPTIMAL SHOOT LENGTH AND PRUNING STRATEGIES IN 'BOURJASOTTE NOIRE' FIG

Bonsai Trees in Your Head: How the Pavlovian System Sculpts Goal-Directed Choices by Pruning Decision Trees

When planning a series of actions, it is usually infeasible to consider all potential future sequences; instead, one must prune the decision tree. Provably optimal pruning is, however, still computationally ruinous and the specific approximations humans employ remain unknown. We designed a new sequential reinforcement-based task and showed that human subjects adopted a simple pruning strategy: during mental evaluation of a sequence of choices, they curtailed any further evaluation of a sequence as soon as they encountered a large loss. This pruning strategy was Pavlovian: it was reflexively evoked by large losses and persisted even when overwhelmingly counterproductive. It was also evident above and beyond loss aversion. We found that the tendency towards Pavlovian pruning was selectively predicted by the degree to which subjects exhibited sub-clinical mood disturbance, in accordance with theories that ascribe Pavlovian behavioural inhibition, via serotonin, a role in mood disorders. We conclude that Pavlovian behavioural inhibition shapes highly flexible, goal-directed choices in a manner that may be important for theories of decision-making in mood disorders.

Optimal pruning for selecting LEDs to synthesize tunable illumination spectra

Multi-channel light-emitting diode (LED) light sources have been developed for various applications in lighting, but especially for spectrum-tunable lighting. However, how to select the optimal combination of LEDs for these light sources is rarely discussed. Unlike the negative-pruning process which operates by removing LEDs from a set of available LEDs based on an unrealizable negative-coefficient criterion alone, the proposed pruning process removes LEDs so as to minimize the synthesis error. This method not only produces the same optimal set of LEDs as those identified by the full-search method but also suggests when using phosphor-converted LEDs is beneficial. It does this by investigating the trade-off between the full width half maximum of the LEDs and the number of LEDs.

Against Classification Attacks: A Decision Tree Pruning Approach to Privacy Protection in Data Mining

Data-mining techniques can be used not only to study collective behavior about customers, but also to discover private information about individuals. In this study, we demonstrate that decision trees, a popular classification technique for data mining, can be used to effectively reveal individuals' confidential data, even when the identities of the individuals are not present in the data. We propose a novel approach for organizations to protect confidential data from such a classification attack. The key components of this approach include a set of entropy-based measures to evaluate disclosure risks of individual records, an optimal pruning algorithm to identify high-risk records, and a pair of data-swapping procedures to reduce the disclosure risks. The proposed method provides the best trade-off between data utility and privacy protection against classification attacks. It can be applied to data with both numeric and categorical attributes. An experimental study on six real-world data sets shows that the proposed method is very effective in protecting privacy while enabling legitimate data mining and analysis.

Yielding capacity and regeneration of different ages fruit-bearing shoots in sour cherry

The yielding potential and regeneration (i.e. germination of hidden buds) after pruning of the fruit-bearing shoots of different ages were compared in sour cherry cultivars pruned to spindle shape. The examinations were carried out in order to determine the optimal pruning strategy resulting in the highest long-term yielding of sour cherry cultivars with intensive crown shape (free and thin spindle shape). According to our results, there are great differences among the studied self-fertile sour cherry cultivars in yielding and regeneration, which are worthwhile to be considered in determining the method and degree of pruning.

Nonmyopic Sensor Scheduling and its Efficient Implementation for Target Tracking Applications

We propose two nonmyopic sensor scheduling algorithms for target tracking applications. We consider a scenario where a bearing-only sensor is constrained to move in a finite number of directions to track a target in a two-dimensional plane. Both algorithms provide the best sensor sequence by minimizing a predicted expected scheduler cost over a finite time-horizon. The first algorithm approximately computes the scheduler costs based on the predicted covariance matrix of the tracker error. The second algorithm uses the unscented transform in conjunction with a particle filter to approximate covariance-based costs or information-theoretic costs. We also propose the use of two branch-and-bound-based optimal pruning algorithms for efficient implementation of the scheduling algorithms. We design the first pruning algorithm by combining branch-and-bound with a breadth-first search and a greedy-search; the second pruning algorithm combines branch-and-bound with a uniform-cost search. Simulation results demonstrate the advantage of nonmyopic scheduling over myopic scheduling and the significant savings in computational and memory resources when using the pruning algorithms.

Small hydro power plant identification using NNARX structure

A feedforward multi-layer perceptron neural network structure is developed to model the nonlinear dynamic relationship between input and output of a hydro power plant connected as single machine infinite bus system. Two independent second-order neural network nonlinear auto-regressive with exogenous signal models are used in the study. The structure selection of each independent model is based on various validation tests. The optimal brain surgeon pruning strategy adopted for optimizing the neural network structure. The network performance is studied for fixed and change in operating point.

An evaluation of the radial part of numerical integration commonly used in DFT.

Recently, Gill and Chien introduced a new radial quadrature for multiexponential integrands (MultiExp grid) to deal with the radial part of the numerical integration. In this article, the MultiExp grid is studied and used to integrate the charge density. The MultiExp grid, along with an optimal pruning scheme, performed very well both in terms of accuracy and efficiency compared to other radial mappings commonly used in Density Functional Theory.

The Difficulty of Reduced Error Pruning of Leveled Branching Programs

Induction of decision trees is one of the most successful approaches to supervised machine learning. Branching programs are a generalization of decision trees and, by the boosting analysis, exponentially more efficiently learnable than decision trees. However, this advantage has not been seen to materialize in experiments. Decision trees are easy to simplify using pruning. Reduced error pruning is one of the simplest decision tree pruning algorithms. For branching programs no pruning algorithms are known. In this paper we prove that reduced error pruning of branching programs is infeasible. Finding the optimal pruning of a branching program with respect to a set of pruning examples that is separate from the set of training examples is NP-complete. Because of this intractability result, we have to consider approximating reduced error pruning. Unfortunately, it turns out that even finding an approximate solution of arbitrary accuracy is computationally infeasible. In particular, reduced error pruning of branching programs is APX-hard. Our experiments show that, despite the negative theoretical results, heuristic pruning of branching programs can reduce their size without significantly altering the accuracy.

Bud-, flower- and fruit-density in stone fruits

In 164 varieties of five stone fruit species, counts of flower buds, flowers and fruits set have been performed, regularly, between 1982 and 2002. The critical number and sample size has been determined for the purpose to estimate the yielding potential of peach plantations. For a rapid test, 10 shoots per variety are recommended. In sour cherry and peach varieties, the number and ratio of leaf and flower buds has been assessed on bearing shoots of different length.
 The typical flower bud density of 129 peach varieties varies, as a rule, between 0.13 and 1.10 bud/cm. Three groups of flower-bud-densities could be distinguished: low (0-0.40 bud/cm), intermediate (0.41-0.60 bud/cm), high (more than 0.60 bud/cm). About 62% of varieties belong to the intermediate group. Negative correlation has been found between flower density and relative fruit set, whereas positive correlation between flower density and fruit yield.
 The results are utilised in the description and choice of varieties, moreover, in choosing of optimal pruning policies. Varieties of high flower bud densities are recommended to be preferred for growing sites with frequent late frosts. Abundantly yielding varieties of low vegetative vigour are to be pruned more severely than those characterised by low yields, vigorous growth and low flower density. Sour cherry varieties, which are inclined to grow "whips" ought to be stimulated to grow longer shoots (40-50 cm per year), than varieties woid of that tendency (30-40 cm).

Optimal pruning in neural networks

We study pruning strategies in simple perceptrons subjected to supervised learning. Our analytical results, obtained through the statistical mechanics approach to learning theory, are independent of the learning algorithm used in the training process. We calculate the post-training distribution P(J) of synaptic weights, which depends only on the overlap rho(0) achieved by the learning algorithm before pruning and the fraction kappa of relevant weights in the teacher network. From this distribution, we calculate the optimal pruning strategy for deleting small weights. The optimal pruning threshold grows from zero as straight theta(opt)(rho(0), kappa) approximately [rho(0)-rho(c)(kappa)](1/2) above some critical value rho(c)(kappa). Thus, the elimination of weak synapses enhances the network performance only after a critical learning period. Possible implications for biological pruning phenomena are discussed.

Biometric relationships and growth of pruned and non-pruned Acacia saligna under runoff irrigation in northern Kenya

The objective of this study was to compare allometric equations for pruned and non-pruned Acacia saligna (Labill.) H.L. Wendl. and to evaluate their possible use in the prediction of optimum pruning intervals. The necessary data were obtained from a field experiment carried out in the Turkana District of Kenya where the objective was to examine the production potential of runoff agroforestry systems. Trees were planted at different densities (2500 and 833 trees ha −1), pruned or not, and intercropped or grown in sole stands. Measurements of cross sectional area (CSA) at the trunk base were taken at monthly intervals. Intermediate biomass yields were obtained twice during the experimental period by complete pruning of the trees at 1.5 m height and by harvesting of whole trees at the end of the experiment. Linear regressions of CSA versus biomass yield were established for whole trees, individual plant organs (leaves, branches and trunks) for both pruned and non-pruned trees. Similar slopes were found for the relationships between CSA and total above ground biomass of non-pruned trees and between the increase in CSA and the total above ground biomass of trees after pruning. These results suggest that the regression coefficients obtained for non-pruned Acacia saligna trees can be used to estimate the regrowth of pruned trees. The allometric equations were used to calculate average daily increments of plant growth (ADI) and relative growth rates (RGR). During the trial, ADI's were higher for trees planted at low density. RGR's clearly responded to the pruning treatments. Five months after the first pruning was carried out, the RGR of pruned trees were higher than those of non-pruned trees and increasing, as opposed to those of non-pruned trees which were decreasing. RGR is a simple tool that allows the determination of optimal pruning intervals. We used the allometric equations to compute RGR and suggest that this approach is appropriate to determine pruning intervals in agroforestry systems. In our study we found that the imposed pruning intervals were too short and suggest an optimal range of 6–8 months.

CONTROLLING YIELD AND FRUIT QUALITY IN MAIGOLD APPLE ORCHARDS

A major problem with the profitability of modern fruit crop lies in the possibility of ensuring an even level of production. This goal is not easy to achieve with strongly alternating cultivars like Maigold. A better understanding of the behaviour of an orchard submitted to various management strategies has been reached as a result of a trial carried out at the Centre des Fougeres, from 1986 onwards, with the cv. Maigold grafted on M27 rootstock. Four treatments have been tested : three of them combine optimal (long) pruning and three levels of fruit load (minimal, optimal and heavy). The fourth combines severe (short) pruning and heavy load. The highest and most even yields during the whole experimental period were those obtained while managing the fruit load as suggested in the treatment optimal pruning and fruit load. However, the initial objective for fruit load proved too generous and should be lowered (5,5 fruits/cm 2 of stem cross area, instead of 6,5). The plots with heavy load showed a strong altemance and a break down in yields. Limiting fruit load through excessive thinning (3,5 fruits/cm 2 of stem cross area) avoid biennial bearing but results in poor yields and commercial losses due to excessively large fruits which are discarded. Light pruning and proper load restriction allow for sustained yield of high quality fruits. An excessively severe load restriction results in production of large, commercially discarded fruits. The absence of load restriction results in fruiting alternance and bad fruit quality. An even very severe pruning in not a valuable alternative to load restriction through fruit thinning.

An efficient algorithm for optimal pruning of decision trees

Pruning decision trees is a useful technique for improving the generalization performance in decision tree induction, and for trading accuracy for simplicity in other applications. In this paper, a new algorithm called OPT-2 for optimal pruning of decision trees is introduced. The algorithm is based on dynamic programming. In its most basic form, the time and space complexities of OPT-2 are both Θ ( nC), where n is the number of test nodes in the initial decision tree, and C is the number of leaves in the target (pruned) decision tree. This is an improvement over the recently published OPT algorithm of Bohanec and Bratko (which is the only known algorithm for optimal decision tree pruning) especially in the case of heavy pruning and when the tests of the given decision tree have many outcomes. If so desired, the space required by OPT-2 can further be reduced by a factor of r at the cost of increasing the execution time by a factor that is bounded above by (r + 1) 2 (this is a considerable overestimate, however). From a practical point of view, OPT-2 enjoys considerable flexibility in various aspects, and is easy to implement.

Demographic approaches to studies of canopy development in plants

Via their modular structure, plants operate at two levels in their population biology—the level of the individual and that of the parts which make up an individual; the genet and the ramet ( sensu Harper). Thus, possibilities exist to describe the growth of plants as a population-like process rather than via the conventional notions of dry matter change and relative growth rate. This paper gives three applications of this idea. The first analyses the temporal changes in the number of vegetative and flowering shoot meristems of plants grown in different soil volumes. The main conclusion was that the ‘trade-off’ between the production of flowering or vegetative meristems was less influenced by root restriction than was the overall production of meristems. This was higher for plants grown in the largest pots. The second example is an analysis of pruning apple trees where, using bud-counts on pruned and unpruned trees, bud distribution between branches was analysed. Pruning restored a normal distribution, whereas unpruned plants had a skewed distribution of buds per branch. The final, related notion, is the development of a matrix model of bud pruning based on the prediction of the maximum harvestable yield of an animal population. Pruning and harvesting are analagous processes since both involve removal of some individuals, thus affecting the fecundity or productivity of remaining members of the population. Optimal pruning or harvesting estimates, on the basis of the age-dependent fecundity and survival of individuals in the population, the maximum number of individuals which can be removed without reducing the overall population growth rate below unity. At this point, all harvested individuals or pruned buds are replaced in the next time step. The discussion highlights directions for extending this corollary further.

Some issues related to fixed-rate pruned tree-structured vector quantizers

It is shown that the generalized BFOS algorithm is not optimal when it is used to design fixed-rate pruned tree-structured vector quantizers (PTSVQ). A simple modification is made in the algorithm which makes it optimal. However, experimental results show little difference between the rate-distortion curves generated with the original algorithm and the one proposed in the present paper. An asymptotic analysis is presented which shows how the two algorithms prune the TSVQ and explains why their results are so similar. The analysis also shows that in designing fixed-rate variable-depth TSVQs one can get as good a rate-distortion performance with a greedy TSVQ growing algorithm as with the optimal pruning of a large tree. >

Growing and pruning neural tree networks

A pattern classification method called neural tree networks (NTNs) is presented. The NTN consists of neural networks connected in a tree architecture. The neural networks are used to recursively partition the feature space into subregions. Each terminal subregion is assigned a class label which depends on the training data routed to it by the neural networks. The NTN is grown by a learning algorithm, as opposed to multilayer perceptrons (MLPs), where the architecture must be specified before learning can begin. A heuristic learning algorithm based on minimizing the L1 norm of the error is used to grow the NTN. It is shown that this method has better performance in terms of minimizing the number of classification errors than the squared error minimization method used in backpropagation. An optimal pruning algorithm is given to enhance the generalization of the NTN. Simulation results are presented on Boolean function learning tasks and a speaker independent vowel recognition task. The NTN compares favorably to both neural networks and decision trees.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal pruning for tree-structured vector quantization

Tree-structured vector quantization (VQ) is a technique designed to represent a codebook that simplifies encoding as well as vector quantizer design. Most design algorithms for tree-structured VQ used in the past are based on heuristics that successively partition the input space. Recently, Chou, Lookabaugh and Gray proposed a tree-pruning heuristic in which a given initial tree is pruned backwards according to certain optimization criterion. We define the notion of an optimal pruned tree subject to a cost constraint and study the computational complexity of finding such an optimal tree for various cost functions. Under the assumption that all trees are equally probable, we show that, on the average, the number of pruned trees in a given tree is exponential in the number of leaves. Furthermore, we prove that finding an optimal pruned tree subject to constraints such as entropy or the expected-depth is NP-hard. However, we show that when the constraint is the number of leaves, the problem can be solved in polynomial time. We develop an algorithm to find the optimal pruned tree in O(nk) time, where n is the size of the initial tree and kis the constraint size.

Recursive optimal pruning with applications to tree structured vector quantizers

A pruning algorithm of P.A. Chou et al. (1989) for designing optimal tree structures identifies only those codebooks which lie on the convex hull of the original codebook's operational distortion rate function. The authors introduce a modified version of the original algorithm, which identifies a large number of codebooks having minimum average distortion, under the constraint that, in each step, only modes having no descendents are removed from the tree. All codebooks generated by the original algorithm are also generated by this algorithm. The new algorithm generates a much larger number of codebooks in the middle- and low-rate regions. The additional codebooks permit operation near the codebook's operational distortion rate function without time sharing by choosing from the increased number of available bit rates. Despite the statistical mismatch which occurs when coding data outside the training sequence, these pruned codebooks retain their performance advantage over full search vector quantizers (VQs) for a large range of rates.

Variable rate vector quantization for medical image compression

Three techniques for variable-rate vector quantizer design are applied to medical images. The first two are extensions of an algorithm for optimal pruning in tree-structured classification and regression due to Breiman et al. The code design algorithms find subtrees of a given tree-structured vector quantizer (TSVQ), each one optimal in that it has the lowest average distortion of all subtrees of the TSVQ with the same or lesser average rate. Since the resulting subtrees have variable depth, natural variable-rate coders result. The third technique is a joint optimization of a vector quantizer and a noiseless variable-rate code. This technique is relatively complex but it has the potential to yield the highest performance of all three techniques.